Regime-Switching Recombining Tree for Option Pricing

Abstract

In this paper we develop an efficient tree approach for option pricing when the underlying asset price follows a regime-switching model. The tree grows only linearly as the number of time steps increases. Thus it enables us to use large number of time steps to compute accurate prices for both European and American options. We present conditions that guarantee the positivity of branch probabilities. We numerically test the sensitivity of option prices to the choice of a key parameter for tree construction. As an interesting application, we develop a regime-switching model to approximate the Heston's stochastic volatility model and then employ the tree approach to approximate the option prices. Numerical results are provided and compared.

A new efficient numerical method for solving American option under regime switching model

“…However, In order to compare the solution with penalty and lattice methods described in [23], Table 1 [23]. Table 1 shows that our results are close to both methods especially to the binomial model of [26].…”

“…Lattice methods [19,26] are popular for practitioners because they are easy to implement, but they have the drawback of the absence of numerical analysis and subsequent unreliability, because the lack of numerical analysis 35 may waste the best model. The penalty method [18,22,23,34] uses a coupling of the penalty term and the regime coupling terms.…”

Laplace Transform Methods for a Free Boundary Problem of Time-Fractional Partial Differential Equation System

“…Markov regime switching models were first introduced by Hamilton [1] and recently have become popular in financial applications including equity options [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], bond prices and interest rate derivatives [18][19][20], portfolio selection [21], and trading rules [22][23][24][25][26]. The Markov regime switching models allow the model parameters (drift and volatility coefficients) to depend on a Markov chain which can reflect the information of the market environments and at the same time preserve the simplicity of the models.…”

Finite Difference Methods for nonlinear American Option Pricing models: Numerical Analysis and Computing

“…Lattice methods [87,114] are popular for practitioners because they are easy to implement, but they have the drawback of the absence of numerical analysis and subsequent unreliability, because the lack of numerical analysis may waste the best model. The penalty method [57,70,71,116] uses a coupling of the penalty term and the regime coupling terms.…”

“…In order to compare the solution with penalty and lattice methods described in [70], Table 3.6 contains option prices for different values of asset price S computed by: our proposed front-fixing explicit method (FF-expl), the exponential time differencing Crank-Nicolson scheme (ETD-CN) and the binomial tree approach developed by Liu in [87] (Tree). This binomial tree model has the good property that tree only grows linearly as the number of time steps increases allowing the use of large number of time steps to compute accurately prices of options.…”